This is anecdotal evidence but Dennis Rodman (the pro basketball player) was the greatest rebounder of all time. One of his teammates related to how he would watch guys shoot (usually during warmups) and count the rotation of the ball. Based on how many times the ball would rotate, he knew if it was going in or not and then would position himself to get the rebound.

I would imagine OP did something similar. Watch the coin as its rotating and then grabbing it and then flipping to the side he predicted.

I knew someone else who could do this pretty reliably. He said it was a “feel the timing” thing. Best analogy he had was maybe like landing an ice skating triple jump, or a complex dive. It happens too fast to be consciously controlled. Instead the trick is to train the body to get a feel for success and then just let the body do it.

It's easy. All you need to do is rotate (yaw) your hand when flipping so that the coin spins but never actually flips, or a little slower so it flips only once. A watchful eye can detect it happening, though.

You can preview the effect by spinning a coin slowly on a table.

This is a common problem in intro Physics Mechanics class.